I have a multinomial population of twins (either identical or not) from which I have taken a sample of n. n1 are MM, n2 are FF, n3 are MF but we don't know which are identical (probability that twins are identical = alpha, male/female twins are non-identical, equally likely that identical twins are MM or FF).
P(MM) = P(FF) = (1+alpha)/4 and P(MF) = (1-alpha)/2

I have found the MLE of alpha for the sample (n1+n2-n3)/(n1+n2+n3) but I have no idea how to find its variance??
My starting point was Var(MLE) = E(MLE^2) - E(MLE)^2, but I'm not sure if this is correct or where to go from here....

Any help would be much appreciated :)

Hint: Multinomial distribution.. see the link below for more information.
http://en.wikipedia.org/wiki/Multinomial_distribution

Ok I'm not entirely sure how the multinomial population is supposed to help but I have tried to work something out based on the fact that for the multinomial population Var(xi)=npi(1-pi)....

Since E(ni) = n*alpha, Var(ni) = Var(n*alpha) = n^2Var(alpha)
So Var(alpha) = n*alpha(1-alpha)/n^2 = alpha(1-alpha)/n

Uncertain whether this is correct and whether it applies to the MLE or the population alpha...

Given n ( n=n1+n2+n3) ,the above is a multinomial distribution.

where E(ni) = n * pi
ie E(n1) = n*p1 = n * (1+alpha)/4

Now you have to calculate the variance of (n1+n2-n3 )/n where n is given. ( here n1 , n2 ,n3 are not independent ).